How do I solve the Partial differential equation to calculate Vorticiy?

Flow field: u = V[1 + (h/[Beta]) (2 [Pi]/l) (cos (2 [Pi]x/l)) E^-2 [Pi][Beta]y/l]

v=-V (h) (2 [Pi]/l) (sin (2 [Pi]x/l)) (E^-2 [Pi][Beta]y/l)

I need to solve partial "u" w.r.t partial "y" and partial "v" w.r.t partial "x"

Then I need to show partial u/y - partial v/x = 0. Hence the Vorticity will be zero.

Please see the attached pics. Please help.